What is the derivative of $f (x) = cos (\frac{π}{2} - x)$ $f(x)=cos(pi/2-x)$ ?

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Answer 1 · 2017-02-22T00:26:58

$\frac{d}{d x} cos (\frac{π}{2} - x) = cos x$ $d/dx cos (pi/2-x) = cosx$

Using the trigonometric formula:

$cos (α - β) = cos α cos β + sin α sin β$ $cos(alpha-beta) = cos alpha cos beta + sin alpha sin beta$

we have:

$cos (\frac{π}{2} - x) = sin x$ $cos (pi/2-x) = sinx$

so:

$\frac{d}{d x} cos (\frac{π}{2} - x) = \frac{d}{d x} sin x = cos x$ $d/dx cos (pi/2-x) = d/dx sinx = cosx$

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